What is the integral of (e^r)/(1+e^r) ?

The integral of (e^r)/(1+e^r) is ln|1+e^r|+C

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integral of (e^r)/(1+e^r)

\int \frac{e ^{r}}{1 + e ^{r}} d r

ln ∣ 1 + e^{r} ∣ + C

Solution steps

\int \frac{e ^{r}}{1 + e ^{r}} d r

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = 1 + e^{r}

= ln ∣ 1 + e^{r} ∣

Add a constant to the solution

= ln ∣ 1 + e^{r} ∣ + C

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What is the integral of (e^r)/(1+e^r) ?
The integral of (e^r)/(1+e^r) is ln|1+e^r|+C